Finite Group Databasebeta

← #11778758

Subgroups — #11778758

Order 1152.

461 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 461 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594980C211yesmaximal, characteristic
2C3×#4722C211yesmaximal, characteristic, complemented
3#10591225C211yesmaximal, characteristic, complemented
4#10591125C211yesmaximal, characteristic
5#10589336C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#71178—31nomaximal
9#68136—31nomaximal
10#64139C2211yescharacteristic
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14#63966—21no—
15#63952—21no—
16#63897—21no—
17#63888—21no—
18#63848—21no—
19#63845—21no—
20C32×C22⋊C8C2211yescharacteristic
21#63658C2211yescharacteristic
22C3×#830C2211yescharacteristic
23C3×#818—21no—
24C3×#816—21no—
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63564—21no—
29#5645—31no—
30#5515—31no—
31C3×#484—31no—
32#4986—31no—
33#4985—31no—
34#4968—31no—
35#4735—31no—
36#4722D311yescharacteristic, complemented
37C3×#324—31no—
38#4538—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4469D311yescharacteristic, complemented
43#4467—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#624—21no—
53C2×C32×C8—21no—
54#3752—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—21no—
70Dic32—21no—
71#1615—91noSylow
72C3×C22⋊Q8—31no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75#946—61no—
76#930—31no—
77#930—31no—
78#930—61no—
79#929—61no—
80C4×#67—61no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82#924C2×D311yescharacteristic
83C2×Dic3⋊C4C2×D311yescharacteristic
84#898—61no—
85#898—61no—
86#896—61no—
87#894—61no—
88#894—61no—
89#890—61no—
90#889—61no—
91#886—61no—
92#67⋊C4—61no—
93C3×#107—61no—
94C3×#103—61no—
95C3×C22⋊C8—21no—
96C3×C22⋊C8—31no—
97C3×C22⋊C8C2×D311yescharacteristic
98C3×C22⋊C8C2×D311yescharacteristic
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106#830C2×D311yescharacteristic
107#821—61no—
108#818—21no—
109#817—61no—
110#816—21no—
111#809—61no—
112#808—61no—
113C23×C32C2×D411yescharacteristic
114C22×C3⋊D3—21no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118#638—41no—
119#638—41no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C4⋊(C3⋊D3)—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—41no—
134C3×Dic6—41no—
135#624—81no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#539—91no—
139#484—31no—
140#481—91no—
141#400—91no—
142#328—91no—
143#327—91no—
144#324—31no—
145C2×C3×Q8—31no—
146C22×C3×C4—21no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—61no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C2×#67—61no—
153C2×#67—61no—
154C2×#67—121no—
155C22×Dic3—21no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C22×Dic3—121no—
159C22×Dic3D1211yescharacteristic
160C22×Dic3D1211yescharacteristic
161C2×D12—31no—
162C2×D12—31no—
163C2×D12—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×Dic6#6711yescharacteristic
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178#217—21no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—121no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3—31no—
191C4⋊Dic3—31no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3#6711yescharacteristic
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C2×C3⋊C8—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#12011yescharacteristic
209C22×C32#13511yescharacteristic
210C22×C32#13711yescharacteristic
211C2×C3⋊D3—41no—
212C2×C3⋊D3—41no—
213C2×C3⋊D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C3⋊Dic3—41no—
217C3⋊Dic3—81no—
218C3×Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223#126—181no—
224#125—181no—
225#123—181no—
226#123—181no—
227C22⋊Q8—31no—
228C22⋊Q8—181no—
229#121—91no—
230C4×D4—181no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233#107—61no—
234#106—181no—
235#103—61no—
236#102—181no—
237C22⋊C8—31no—
238C22⋊C8D3211yescharacteristic
239#95—91no—
240#95—181no—
241#95—181no—
242C23×C3—21no—
243C23×C3C2×D1211yescharacteristic
244C23×C3D3×D411yescharacteristic
245C22×D3—61no—
246C22×D3—61no—
247C22×D3—121no—
248C3×Q8—121no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—81no—
260C2×C3×C4—121no—
261C2×C3×C4—122no—
262C2×C3×C4—121no—
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267#67—121no—
268#67—121no—
269#67—121no—
270#67—121no—
271#67—241no—
272#67—241no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—41no—
280C2×Dic3—42no—
281C2×Dic3—41no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3—121no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—122no—
290C2×Dic3—121no—
291C2×Dic3—121no—
292C2×Dic3—241no—
293C2×Dic3—241no—
294D12—121no—
295D12—121no—
296D12—241no—
297C4×D3—241no—
298C4×D3—241no—
299Dic6—41no—
300C3×C8—41no—
301C3×C8—41no—
302C3×C8—81no—
303C3×C8—121no—
304C3⋊C8—41no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32#45211yescharacteristic
308C2×C32#45411yescharacteristic
309C2×C32#45811yescharacteristic
310C3⋊D3—81no—
311C2×Q8—31no—
312C2×D4—91no—
313C2×D4—181no—
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—61no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4C2×D3211yescharacteristic
320C2×C8—21no—
321C2×C8—61no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—91no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—61no—
333C22⋊C4—181no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C42—181no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3#88211yescharacteristic
348C22×C3#90411yescharacteristic
349C22×C3#90911yescharacteristic
350C22×C3#91811yescharacteristic
351C22×C3#91911yescharacteristic
352C22×C3#93711yescharacteristic
353C2×D3—121no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—241no—
360C2×D3—241no—
361C2×D3—241no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—121no—
369C3×C4—121no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4—241no—
373Dic3—41no—
374Dic3—41no—
375Dic3—41no—
376Dic3—41no—
377Dic3—81no—
378Dic3—121no—
379Dic3—121no—
380Dic3—241no—
381Dic3—241no—
382Dic3—241no—
383Dic3—242no—
384C32#161511yescharacteristic, complemented, Sylow
385C23—181no—
386C23D3×D1211yescharacteristic
387Q8—121no—
388D4—361no—
389D4—361no—
390D4—361no—
391C2×C4—41no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—121no—
399C2×C4—122no—
400C2×C4—121no—
401C2×C4—181no—
402C2×C4—361no—
403C2×C4—361no—
404C2×C4—361no—
405C2×C4—721no—
406C2×C4#380211yescharacteristic
407C2×C4D3×#6711yescharacteristic
408C8—41no—
409C8—121no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3#473311yescharacteristic
420C2×C3#474211yescharacteristic
421C2×C3#475311yescharacteristic
422C2×C3#505311yescharacteristic
423C2×C3#518711yescharacteristic
424C2×C3#520111yescharacteristic
425D3—241no—
426D3—241no—
427D3—481no—
428C22—21no—
429C22—21no—
430C22—361no—
431C22—361no—
432C22—361no—
433C22#6380111yescharacteristic
434C22#6380811yescharacteristic
435C22#6392211yescharacteristic
436C4—21no—
437C4—21no—
438C4—121no—
439C4—121no—
440C4—121no—
441C4—121no—
442C4—241no—
443C4—361no—
444C4—721no—
445C3—21no—
446C3#6813611yescharacteristic, complemented
447C3#7117811yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—721no—
451C2#1059040811yescharacteristic
452C2#1059096611yescharacteristic
453C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#64139C22
hypercenterC22⋊C8D32
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#4722C2semidirect
3. #10591225C2semidirect
6. C3×#4469C2semidirect
7. #10589152C2semidirect
36. #4722D3semidirect
42. #4469D3semidirect
384. C32#1615semidirect
446. C3#68136semidirect
447. C3#71178semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105949802
C3×#47222
#105912252
#105911252
#105893362
C3×#44692
#105891522
#711783
#681363